Formally Verified Patent Analysis via Dependent Type Theory: Machine-Checkable Certificates from a Hybrid AI + Lean 4 Pipeline

2026-04-19 · Source: cs.AI updates on arXiv.org · Field: Legal & Regulatory — Intellectual Property & Patents, Legal Technology (LegalTech), Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

This paper introduces a formally verified framework for patent analysis, combining AI/NLP methods with interactive theorem proving using Lean 4. The framework encodes patent claims as directed acyclic graphs (DAGs) in Lean 4, models match strengths as elements of a complete lattice, and propagates confidence scores using formally verified monotone functions. It formalizes five intellectual property (IP) use cases: patent-to-product mapping, freedom-to-operate, claim construction sensitivity, cross-claim consistency, and doctrine of equivalents. The core DAG-coverage component (Algorithm 1b) is fully machine-verified, providing machine-checkable certificates for computational correctness given ML-produced scores. The formal guarantees are conditional on the ML layer's semantic accuracy, but offer a qualitatively stronger assurance than purely probabilistic systems. A case study on a synthetic memory-module claim demonstrates the framework's application, including weighted coverage computation and claim-construction sensitivity analysis.

Key takeaway

For research scientists developing high-stakes AI systems, you should consider adopting a hybrid architecture that formally verifies structured computational components, even when relying on ML for natural language understanding. This approach, demonstrated in patent analysis, provides machine-checkable proof certificates and explicit trust boundaries, offering stronger, auditable guarantees than purely probabilistic systems. Focus on isolating and verifying the deterministic parts of your workflow to enhance trustworthiness and reproducibility.

Key insights

A hybrid AI + Lean 4 pipeline provides machine-verified certificates for patent analysis computations, given ML-derived inputs.

Principles

• Separate proof generation (untrusted) from proof checking (trusted).
• Structured computation can be formally verified, even with ML inputs.
• Acyclic dependency graphs enable well-founded recursive definitions.

Method

Encode patent claims as Lean 4 DAGs, model match strengths as a complete lattice, and propagate scores using formally verified functions to generate machine-checkable proof certificates, audited for sorry-free axioms.

In practice

• Use topological sort for efficient DAG propagation in patent analysis.
• Employ a two-step axiom audit to ensure proof certificate validity.
• Discretize continuous scores for exact rational arithmetic in formal proofs.

Topics

• Formal Verification
• Dependent Type Theory
• Lean 4
• Patent Analysis
• Hybrid AI Pipeline

Code references

• leanprover-community/mathlib4

Best for: Research Scientist, AI Scientist, AI Engineer, Legal Professional

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.